Drop deformability

Fig. 22. Spherical drop deformed into an ellipsoidal shape in a rotational shear field [76]...

H.A. Stone 1994, (Dynamics of drop deformation and breakup in viscous fluids), Anna. Rev. Fluid Mech. 26, 65. 

The tensor L defines the character of the flow. The capillary number for the drop deformation and breakup problem is... 

Many authors have worked on drop deformation and breakup, beginning with Taylor. In 1934, he published an experimental work [138] in which a unique drop was submitted to a quasi-static deformation. Taylor provided the first experimental evidence that a drop submitted to a quasi-static flow deforms and bursts under well-defined conditions. The drop bursts if the capillary number Ca, defined as the ratio of the shear stress a over the half Laplace pressure (excess of pressure in a drop of radius R. Pl = where yint is the interfacial tension) ... 

B.J. Bentley and L.G. Leal An Experimental Investigation of Drop Deformation and Breakup in Steady Two-Dimensional Linear Flows. J. Fluid. Mech. 167, 241 (1986). 

Guido, S., Simeone, M., Alfani, A. (2002). Interfacial tension of aqueous mixtures ofNa-caseinate and Na-alginate by drop deformation in shear flow. Carbohydrate Polymers, 48, 143-152. 

To summarize, if the polydisperse emulsion is mainly composed of big drops, even after few seconds of shear, one obtains a well calibrated emulsion (with a mean diameter close to 6 pm) all the drops deform into threads of different... 

Simeone, M., Tassieri, M., Sibillo, V, and Guido, S. 2005. Effect of sol-gel transition on shear-induced drop deformation in aqueous mixtures of gellan and kappa-carrageenan. J. Colloid Interface Sci. 281 488-494. 

Drop deformation occurs when fluid dynamical forces, often referred to as shear forces , in the surrounding fluid act on its surface. Surface and internal viscous forces resist it. Drop dispersion (breakage) occurs when the shear forces exceed the combined resistance force. 

Figure 5. Reduced droplet diameter vs. viscosity ratio. A, in shear and extenslonal flows. The type of shear drop deformation within each of the four zones of X is indicated.

Y. Pawar and K. J. Stebe, Marangoni effects on drop deformation in an extensional flow The role of surfactant physical chemistry. I. Insoluble surfactants, Phys. Fluids 8, 1738-51 (1996). 

A qualitative prediction of the role of the capillary number in drop deformation can be obtained from the normal-stress balance. Now, if the shape is spherical, the capillary term on the right-hand side is a constant, and thus the viscous pressure and stress contributions... 

Now, if the shape is spherical, the capillary term on the right-hand side is a constant, and thus the viscous pressure and stress contributions on the left must also produce a constant value that corresponds to the jump in pressure across the interface that is due to surface tension. In general, however, the pressure and stress differences will not reduce to this very simple form, but will instead vary as a function of position on the surface of the drop. Such a nonuniform distribution of pressure and stress will tend to deform the drop. In fact, in this case, the normal-stress balance can be satisfied only if the drop deforms to a shape where the interface curvature (V n) varies in precisely the same way as the surface pressure and stress difference. 

Figure 8-3. Drop deformation versus time for relaxation of the pair of drops shown in Fig. 2.15. The figure on the right-hand side shows the relaxation data as a function of the actual time. The data on the right-hand side are shown plotted versus a dimensionless time scale, t = t/t, where t = M.

Large-scale simulations of concentrated emulsion flows, Philos. Trans. R. Soc. London Ser. A 361, 813—45 (2003) C. D. Eggleton, T. M. Tsai, and K. J. Stebe, Tip streaming from a drop in the presence of surfactants, Phy. Rev. Lett. 87, 048302/1-4 (2001) X. Li and C. Pozrikidis, Effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow, J. Fluid Mech. 341, 165-94 (1997). 

Problem 8-11. The Effect of Surfactant on Drop Deformation in a General Linear Flow. 

Problem 8-13. Lateral Migration of a Deformable Drop in 2D Poiseuille Flow. A viscous drop of viscosity fi and density p is carried along in the unidirectional motion of an incompressible, Newtonian fluid of viscosity p and density/) = p between two infinite plane walls. The radius of the undeformed drop is denoted as a, and the distance between the walls is d. We assume that the capillary number, Ca = apXl/rr, is small so that the drop deformation is also small. Here, a is the interfacial tension, and G is the mean shear rate of the undisturbed flow. 

Now, if the Reynolds number of the flow is sufficiently small for the creeping-motion approximation to apply, it can be shown by the arguments of Subsection B.3 in Chap. 7 that no lateral motion of the drop is possible unless the drop deforms. In other words, Us = Useiin this case, though, of course, Us is not generally equal to the undisturbed velocity of the fluid evaluated at the X3 position of the drop center. The drop may either lag or lead (in principle) because of a combination of interaction with the walls and the hydrodynamic effect of the quadratic form of the undisturbed velocity profile - see Faxen s law. Because the drop deforms, however, lateral migration can occur even in the complete absence of inertia (or non-Newtonian) effects. In this problem, our goal is to formulate two... 

Single-drop studies have shown that a drop in a rotational shear field will both elongate and undergo internal rotation with increasing shear, until the critical deformation D j, is reached. Beyond this point, breakage occurs. Taylor [56] established the relationship between drop deformation, D, and the magnitude of the rotational shear field. This is shown by Equation (9.46), where P =... 

The dependence of drop deformation on the Weber number and the vorticity inside the drop was studied in [336]. It was shown that the drop is close in shape to an oblate ellipsoid of revolution with semiaxis ratio > 1 If there is no vortex inside the drop, then this dependence complies with the function We(x) given in (2.8.3). The ratio x decreases as the intensity of the internal vortex increases. Therefore, the deformation of drops moving in gas is significantly smaller than that of bubbles at the same Weber number We. The vorticity inside an ellipsoidal drop, just as that of the Hill vortex, is proportional to the distance TZ from the symmetry axis,... 

H. A. Stone, Dynamics of Drop Deformation and Breakup in Viscous Fluids, Annu. Rev. Fluid Mech., 26 (1994). 

At lower gas speed and higher drops surface tension, formation of bag structures and breakup into smaller droplets have been observed following the initial drop deformation into a disk [5], In the current experiment, these smaller drops are not observed, primarily due to the large Weber number. A mist with scales smaller than the camera resolution, which Wcis 1.2 /mi/pixel, was visible both... 

Chou, W.-H., L.-P. Hsiang, and G. M. Faeth. 1997. Dynamics of drop deformation and formation during secondary breakup in the bag breakup regime. AIAA Paper No. 97-0797. 

The use of microrheology for the description of drop deformation and break was found to provide a surprisingly good agreement with experimental observations for the morphology evolution during compounding in a TSE [Utracki and Shi, 1992 Shi and Utracki, 1992, 1993]. The predictive model (without adjustable parameters) was further improved by incorporation of the coalescence... 

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